### Critical Behavior of Non-intersecting Brownian Motions

Claeys T, Neuschel T, Venker M (2020)
COMMUNICATIONS IN MATHEMATICAL PHYSICS 378(2): 1501-1537.

Zeitschriftenaufsatz | E-Veröff. vor dem Druck | Englisch

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Einrichtung
Abstract / Bemerkung
We study n non-intersecting Brownian motions corresponding to initial configurations which have a vanishing density in the large n limit at an interior point of the support. It is understood that the point of vanishing can propagate up to a critical time, and we investigate the nature of the microscopic space-time correlations near the critical point and critical time. We show that they are described either by the Pearcey process or by the Airy line ensemble, depending on whether a simple integral related to the initial configuration vanishes or not. Since the Airy line ensemble typically arises near edge points of the macroscopic density, its appearance in the interior of the spectrum is surprising. We explain this phenomenon by showing that, even though there is no gap of macroscopic size near the critical point, there is with high probability a gap of mesoscopic size. Moreover, we identify a path which follows the Airy(2) process.
Erscheinungsjahr
2020
Zeitschriftentitel
COMMUNICATIONS IN MATHEMATICAL PHYSICS
Band
378
Ausgabe
2
Seite(n)
1501-1537
ISSN
0010-3616
eISSN
1432-0916
Page URI
https://pub.uni-bielefeld.de/record/2945114

### Zitieren

Claeys T, Neuschel T, Venker M. Critical Behavior of Non-intersecting Brownian Motions. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 2020;378(2):1501-1537.
Claeys, T., Neuschel, T., & Venker, M. (2020). Critical Behavior of Non-intersecting Brownian Motions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 378(2), 1501-1537. doi:10.1007/s00220-020-03823-z
Claeys, T., Neuschel, T., and Venker, M. (2020). Critical Behavior of Non-intersecting Brownian Motions. COMMUNICATIONS IN MATHEMATICAL PHYSICS 378, 1501-1537.
Claeys, T., Neuschel, T., & Venker, M., 2020. Critical Behavior of Non-intersecting Brownian Motions. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 378(2), p 1501-1537.
T. Claeys, T. Neuschel, and M. Venker, “Critical Behavior of Non-intersecting Brownian Motions”, COMMUNICATIONS IN MATHEMATICAL PHYSICS, vol. 378, 2020, pp. 1501-1537.
Claeys, T., Neuschel, T., Venker, M.: Critical Behavior of Non-intersecting Brownian Motions. COMMUNICATIONS IN MATHEMATICAL PHYSICS. 378, 1501-1537 (2020).
Claeys, Tom, Neuschel, Thorsten, and Venker, Martin. “Critical Behavior of Non-intersecting Brownian Motions”. COMMUNICATIONS IN MATHEMATICAL PHYSICS 378.2 (2020): 1501-1537.

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